Chocolate Pudding? Serious Hard Math Question!

[b2bw45381]

Hey guys, please help me out. My class was put into groups to figure this problem out and it's our final grade, and my final chance to pass Pre-Al!
Thanks guys!
-------------------------------------
Okay, so a Census taker went to a man's house. She asked what ages the man's three children were.

He said the product of their ages equals 72.
She told him that she still doesnt know what the ages were.

So he adds, the sum of all the ages is the same number as the house number. ((They didnt specify what the house number was))
The Census taker looks at his house number and told him that she still doesnt know their ages.

So then he adds, The oldest one likes chocolate pudding. The Census taker thanked him and said, "Now I know what their ages are." and leaves.

What are the kid's ages?

((Can you please also help me out on how to work the problem? Even if you dont give me the answer because you think that is cheating, can you still help me with how to work it out? Thanks!!!))

[stapel_eliz]

She asked what ages the man's three children were.

He said the product of their ages equals 72.

What are all the possible factors of 72?

From this, what are the possible sets of three numbers which multiply to 72? (Make a list.)

So he adds, the sum of all the ages is the same number as the house number. The Census taker looks at his house number and told him that she still doesnt know their ages.

Add the factors in your list. Which two (or more) sets of factors sum to the same values? (This is your new list.)

So then he adds, The oldest one likes chocolate pudding.

If there is an "oldest" one, then there is one whose age is greater than the other two (who might be twins). Which option on your new list fits this requirement?